What is the first d/(dt)(t^{-1}) ?

The first d/(dt)(t^{-1}) is -1/(t^2)

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d/(dt)(t^{-1})

\frac{d}{d t} (t^{- 1})

- \frac{1}{t ^{2}}

Solution steps

\frac{d}{d t} (t^{- 1})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - 1 \cdot t^{- 1 - 1}

Simplify

- 1 \cdot t^{- 1 - 1} : - \frac{1}{t ^{2}}

= - \frac{1}{t ^{2}}

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